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# Area Questions

Home > Quantitative Aptitude > Area > General Questions
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Two identical circles intersect so that their centers, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is:

A(π/2) â€“ 1

B4

C√2 â€“ 1

D√5

Explanation:

Â We have to find the area of the blue shaded one and double it to get the area common to the both.

Now this can be calculated as Area of the sector OAB - Area of the Triangle OAB.

As OA and OB are perpendicular, area of the sector OAB = 90/360 π (1)^2 = π/4

Area of the triangle OAB = 1/2 * 1 * 1 = 1/2

Area common to both = (π/4 - 1/2)/2 = π/2 - 1

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A rectangle is divided into four rectangles with area 70, 36, 20, and x. The value of x is

A350/9

B350/7

C350/11

D350/13

Explanation:

Areas are in proportion.
70/x = 36/20
=> x = 350/9

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The radius of a circular entertainment park is increased by 1%. What will be the percent increase in its area.

A1%

B22/7%

C44/7%

D2%

Explanation:

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The perimeter of a equilateral triangle and regular hexagon are equal. Find out the ratio of their areas?

A3:2

B2:3

C1:6

D6:1

Explanation:

Given, perimeter of a equilateral triangle and regular hexagon are equal
6r=3a
=> a/r = 2
So Ratio of their areas = (sqrt(3)/4)a^2 : 3sqrt(3)/2 r^2
=> a^2/r^2 : 3*2
=> 4:6 => 2:3

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Find the ratio of the area of square to area of triangle.

A1:2

B2:1

C2:3

D3:2

Explanation:

Let the side of the square = 2 units.
Now the area of the square = 2*2 = 4.
Area of the triangle = 1/2*2*2=2
Ratio = 4 : 2 = 2 : 1.

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The diagonal of a square is twice the side of equilateral triangle. Then the ratio of Area of the Triangle to the Area of Square is?

A?3:8

B?2:5

C?3:6

D?2:4

Explanation:

Diagonal of a square = 2a
Area of the square = 1/2*(diagonal)^2 = 2a^2
Side of the equi triangle is a
Area of equilateral triangle = (_/3/4)a^2
so Ratio of Area of Triangle to Square = (_/3/4)a^2 : 2a^2 = _/3:8

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A circular swimming pool is surrounded by a concrete wall 4ft wide. If the area of the wall is 11/25 of the area of the pool then radius of the pool in feet is

A20

B8

C16

D30

Explanation:

Here is no explanation for this answer

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A square field of side 500 m each is surrounded by a compound wall. A fence is to made such that it encloses a triangle formed by two compound walls and the fence. If the length of the fence is 100m then the maximum possible area in square metres of the triangle can be :

A2500

B10000

C5000

D20000

Explanation:

The triangle has to be max area and hence should be equilateral but cannot be as the angle in the sq shall be 90 degrees. Hence the triangle is isosceles with the angles as 90, 45, 45. Hence the other two sides shall be 50Ö 2 each. So area is 0.5 x base x ht etc. etc.

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The figure below shows 2 concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle touching it at points B, C, D and A. What is the ratio of the Perimeter of the outer circle to that of the polygon ABCD.

Ap/4

B3p/2

Cp/2

Dp

Explanation:

If R is the radius of outer circle, then the side of the innermost square = R. Required answer = 2p r/4r = p /2.

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A circle circumscribes three unit circles that touch each other. What is the area of the larger circle? Note that p is the ratio of the circumference to the diameter of a circle (3.14159265).

A3.14*(7+43?3)

B3.14*(7+3?3)

C3.14*(5+43?3)

DNone of these

Explanation:

By joining centers of 3 unit circles we will get an equilateral triangle of length 2 unit. We have to find the length of the orange line.

And center of the equilateral triangle will be the center of the big circle.

So radius of the big circle will be = (1 + Circum radius of the equilateral triagle)

Formula for Circul radius of the equilateral triangle = 23*(3?2a) here 3?2a is the height of the triangle. a is the side of the triangle

Circum radius of equilateral triangle = 23*3?2*2=23?

Area of big circle will be =?r2=3.14*(1+23?)2 = 3.14*(1+43?+43) =3.14*(1+43?+43) = 3.14*(73+43?)

=3.14*(7+43?3)

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